16 research outputs found
Residue currents of the Bochner-Martinelli type
Our objective is to construct residue currents from Bochner-Martinelli type kernels; the computations hold in the non complete intersection case and provide a new and more direct approach of the residue of Coleff-Herrera in the complete intersection case; computations involve crucial relations with toroidal varieties and multivariate integrals of the Mellin-Barnes type
Multidimensional Fourier Quasicrystals I. Sufficient Conditions
We derive sufficient conditions for an atomic measure where
are positive integers, and is the point measure at
to be a Fourier quasicrystal, and suggest why they may also be
necessary. These conditions extend the necessary and sufficient conditions
derived by Lev, Olevskii, and Ulanovskii for Our methods exploit the
toric geometry relation between Grothendieck residues and Newton polytopes
derived by Gelfond and Khovanskii.Comment: 17 page
Amoebas of complex hypersurfaces in statistical thermodynamics
The amoeba of a complex hypersurface is its image under a logarithmic
projection. A number of properties of algebraic hypersurface amoebas are
carried over to the case of transcendental hypersurfaces. We demonstrate the
potential that amoebas can bring into statistical physics by considering the
problem of energy distribution in a quantum thermodynamic ensemble. The
spectrum of the ensemble is assumed to be
multidimensional; this leads us to the notions of a multidimensional
temperature and a vector of differential thermodynamic forms. Strictly
speaking, in the paper we develop the multidimensional Darwin and Fowler method
and give the description of the domain of admissible average values of energy
for which the thermodynamic limit exists.Comment: 18 pages, 5 figure
Domains of convergence for Ahypergeometric series and integrals
We prove two theorems on the domains of convergence for A-hypergeometric series and for associated
Mellin-Barnes type integrals. The exact convergence domains are described in terms of amoebas and
coamoebas of the corresponding principal A-determinant
Residue currents of the Bochner-Martinelli type
Our objective is to construct residue currents from Bochner-Martinelli type kernels; the computations hold in the non complete intersection case and provide a new and more direct approach of the residue of Coleff-Herrera in the complete intersection case; computations involve crucial relations with toroidal varieties and multivariate integrals of the Mellin-Barnes type